|
%I #26 Nov 29 2019 20:30:43
%S 1,2,3,4,5,243,514,14340,14341,14432,23520,23521,44405,435152,5435254,
%T 12222215,555435035,1053025020422,1053122514003,1435403205450,
%U 1435403205451,1450005114454,2135254510352,2145555022413,2500150125455,133024510545125
%N Base-6 Armstrong or narcissistic numbers, written in base 6.
%C From _M. F. Hasler_, Nov 18 2019: (Start)
%C Whenever a(n) ends in 0 (n = 8, 11, 20, 28), then a(n+1) = a(n) + 1 also satisfies the definition.
%C Like the other single-digit terms, zero would satisfy the definition (n = Sum_{i=1..k} d[i]^k where d[1..k] are the base 6 digits of n), but here only positive numbers are considered. (End)
%H Joseph Myers, <a href="/A010347/b010347.txt">Table of n, a(n) for n = 1..30</a> (the full list of terms, from Winter)
%H Gordon L. Miller and Mary T. Whalen, <a href="https://www.fq.math.ca/Scanned/30-3/miller.pdf">Armstrong Numbers: 153 = 1^3 + 5^3 + 3^3</a>, Fibonacci Quarterly, 30-3 (1992), 221-224.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/NarcissisticNumber.html">Narcissistic Number</a>
%H D. T. Winter, <a href="http://web.archive.org/web/20100109234250/http://ftp.cwi.nl:80/dik/Armstrong">Table of Armstrong Numbers</a> (latest backup on web.archive.org from Jan. 2010; page no longer available), published not later than Aug. 2003.
%o (PARI) A010347=[fromdigits(digits(n,6))|n<-A010348] \\ _M. F. Hasler_, Nov 18 2019
%o (PARI) select( is_A010347(n)={vecmax(n=digits(n+!n))<6 && vecsum([d^#n|d<-n])==fromdigits(n,6)}, [0..10^5]) \\ _M. F. Hasler_, Nov 20 2019
%Y Cf. A010348 (a(n) written in base 10).
%Y In other bases: A010343 (base 4), A010345 (base 5), A010349 (base 7), A010351 (base 8), A010352 (base 9), A005188 (base 10).
%K base,fini,full,nonn
%O 1,2
%A _N. J. A. Sloane_
%E Edited by _Joseph Myers_, Jun 28 2009
|
